Related papers: Quantum thermodynamics and semi-definite optimizat…
We take the perspective of open quantum systems and examine from their nonequilibrium dynamics the conditions when the physical quantities, their relations and the laws of thermodynamics become well defined and viable for quantum many body…
The purpose of this paper is to explore the applications of quantum computing to energy systems optimization problems and discuss some of the challenges faced by quantum computers with techniques to overcome them. The basic concepts…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
We introduce a quantum approximate optimization algorithm (QAOA) for continuous optimization. The algorithm is based on the dynamics of a quantum system moving in an energy potential which encodes the objective function. By approximating…
This work presents a quantum mechanical framework for analyzing quantization-based optimization algorithms. The sampling process of the quantization-based search is modeled as a gradient-flow dissipative system, leading to a…
Discrete combinatorial optimization consists in finding the optimal configuration that minimizes a given discrete objective function. An interpretation of such a function as the energy of a classical system allows us to reduce the…
Semidefinite programming (SDP) is a fundamental convex optimization problem with wide-ranging applications. However, solving large-scale instances remains computationally challenging due to the high cost of solving linear systems and…
We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We…
As the title indicates, this chapter presents a brief, self-contained introduction to five fundamental problems in Quantum Information Science (QIS) that are especially well-suited to be formulated as Semi-definite Programs (SDP). We have…
Quantum thermodynamics aims at extending standard thermodynamics and non-equilibrium statistical physics to systems with sizes well below the thermodynamic limit. A rapidly evolving research field, which promises to change our understanding…
Quantum steering, an intermediate quantum correlation lying between entanglement and nonlocality, has emerged as a critical quantum resource for a variety of quantum information processing tasks such as quantum key distribution and true…
We present a new generic approach to the condensed-matter ground-state problem which is complementary to variational techniques and works directly in the thermodynamic limit. Relaxing the ground-state problem, we obtain semidefinite…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
In this paper we study the relationship between the optimal value of a homogeneous quadratic optimization problem and that of its Semidefinite Programming (SDP) relaxation. We consider two quadratic optimization models: (1) $\min \{x^* C x…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
Operational quantum stochastic thermodynamics is a recently proposed theory to study the thermodynamics of open systems based on the rigorous notion of a quantum stochastic process or quantum causal model. In there, a stochastic trajectory…
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and second law are formulated consistently. In the linear response regime,…
We consider three known bounds for the quadratic assignment problem (QAP): an eigenvalue, a convex quadratic programming (CQP), and a semidefinite programming (SDP) bound. Since the last two bounds were not compared directly before, we…
Classical thermodynamics is built with the concept of equilibrium states. However, it is less clear how equilibrium thermodynamics emerges through the dynamics that follows the principle of quantum mechanics. In this paper, we develop a…
The new scheme employed (throughout the thermodynamic phase space), in the statistical thermodynamic investigation of classical systems, is extended to quantum systems. Quantum Nearest Neighbor Probability Density Functions are formulated…